n-Type thermoelectric metal chalcogenide (Ag,Pb,Bi)(S,Se,Te) designed by multi-site-type high-entropy alloying

Abstract

A metal chalcogenide (Ag,Pb,Bi)(S,Se,Te) with an NaCl-type structure was designed by multi-site-type high-entropy alloying (MST-HEA), and the thermoelectric properties were investigated. In this material, both cation and anion sites were alloyed and thus its total entropy of mixing ΔS_mix (total) achieved 2.00R (R: gas constant). It was found that present sample is an n-type semiconductor with ultra-low lattice thermal conductivity (κ_L) of 0.62 Wm⁻¹K⁻¹ at room temperature and 0.46 Wm⁻¹K⁻¹ at T = 723 K. Very low κ_L and good power factor resulted in figure of merit of 0.54 at T = 723 K.

IMPACT STATEMENT

We report on the material design synthesis and thermoelectric properties on new high-entropy alloy-type compound with an NaCl-type structure (Ag,Pb,Bi)(S,Se,Te)

KEYWORDS:

• High-entropy-alloy
• material design
• new thermoelectric material
• NaCl-type structure

Introduction

Thermoelectric generators have attracted much attention due to their direct conversion of heat into electricity vice versa. The conversion efficiency of a thermoelectric material depends primarily on the dimensionless figure of merit, ZT = (S²Tρ⁻¹κ_total⁻¹), where S, T, ρ and κ_total are the Seebeck coefficient, absolute temperature, electrical resistivity and thermal conductivity, respectively [1]. κ_total has two main components, namely κ_e and κ_L, which are carrier and lattice thermal conductivity, respectively. To realize the high ZT value, it is obvious that low ρ and high S are essential, although they depend on the carrier concentration and contradict each other. Another main strategy is realization of low κ_L because κ_L is independent of the electronic properties.

Metal chalcogenides (MCh) such as lead chalcogenides (PbTe, PbSe, PbS) have extensively studied as a thermoelectric system available at medium temperature (500–900 K) range [2–4]. The attempts to enhance the thermoelectric properties of MCh have been made by nano-structuring [5] and phase solution of pseudo-binary PbTe-PbSe [6–8] and ternary PbTe–PbSe–PbS [9,10] alloys, which achieve low κ_L and lead to improvements in power factor by band convergence [1,6,7]. In addition to the above-mentioned strategy, the introduction of bonding heterogeneity and the enhancement of lattice anharmonicity have been reported in AgPbBiSe₃ [11] with quite low κ_L of 0.50 Wm⁻¹K⁻¹ at room temperature and 0.41 Wm⁻¹K⁻¹ at 818 K. The fundamental origin of this ultra-low κ_L is originated from the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s² lone pairs of Bi and Pb [11].

As a brand-new method of alloying, high-entropy alloys (HEAs) have attracted much attention in the fields of materials science and engineering because of their tunable properties as structural materials, such as excellent mechanical performance under extreme conditions [12,13]. HEAs are typically defined as alloys containing at least five elements with concentrations between 5 and 35 at%, resulting in high configurational mixing entropy (ΔS_mix), defined as ΔS_mix = -RΣ_ic_ilnc_i, where c_i and R are the compositional ratio and the gas constant, respectively [13]. Most of HEA materials are structurally simple alloys with bcc, α-Mn, CsCl, and hcp crystal structures have mainly been studied so far [12–14]. Thus far, we have extended the concept of HEA to compounds, for instance layered structure and non-layered compounds of NaCl-type metal chalcogenide, as superconductors with high ΔS_mix [15–22]. Furthermore, as an efficient way to increase total entropy of mixing, we proposed multi-site alloying of compounds and its evaluation way by summing the entropy of mixing at each alloying site [20]. A higher ΔS_mix, which exceeds the typical ΔS_mix for equimolar 6 elements for single site, is achieved by this method. It is well known that alloying is the effective way to reduce κ_L due to the enhancement of scattering of phonons by lattice disorder [8,23]. Based on this fact, the high-entropy alloying by the multi-site alloying method also could be the effective way to reduce the κ_L, for instance, by introducing the severe lattice distortion [24].

As HEA thermoelectric materials, AlCoCrFeNi [25] was first reported by Shafeie et al. in 2015. However, the ZT values are low due to the high σ, low S and high κ. After the report, some papers incorporating the HEA concept into thermoelectric materials have been reported: such as half-Huesler; NdFeSb-based [26], Ti₂NiCoSnSb [27] and MCh; AgSnSbSe_3-xTe_x [28]. Among them, AgSnSbSe_3-xTe_x exhibited high ZT values of 1.14 at 723 K as p-type thermoelectric materials. Very recently, n-type MCh of Pb_0.99−ySb_0.012Sn_ySe_1−2xTe_xS_x was reported with significantly high ZT values of 1.8 at 900 K [29]. On this basis, we aimed to synthesize new NaCl-type MCh with higher ΔS_mix value.

In this letter, we synthesized a high-entropy alloy-type (Ag,Pb,Bi)(S,Se,Te) by inducing alloying an anion site of n-type AgPbBiSe₃ with low κ_L. Hereafter, we denote the concept that alloying multiple crystallographic site as ‘multi-site-type high-entropy alloying (MST-HEA)’. We successfully synthesized MST-HEA (Ag,Pb,Bi)(S,Se,Te) with highest ΔS_mix (total) value of 2.00R as a thermoelectric material to the best of our knowledge. It was found that the present sample was an n-type semiconductor with ultra-low κ_L of 0.62 Wm⁻¹K⁻¹ at room temperature, and it reached 0.46 Wm⁻¹K⁻¹ at 723 K. Compared to AgPbBiSe₃, the present sample exhibited lower ρ without large decrease of S, resulted in the enhancement of power factor and ZT. Our results indicate that the MST-HEA MCh could be a promising n-type thermoelectric material.

Experimental

Polycrystalline sample of (Ag,Pb,Bi)(Te,Se,S) was synthesized by congruent melt of Ag powders (99.9%) and grains of Pb (99.9%), Bi (99.999%), Te (99.999%), Se (99.99%) and S (99.9999%) with a nominal composition of Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 at 800°C for 20 h after keeping at 400 °C for 5 h to suppress an evaporation of chalcogen in an evacuated quartz tube. To obtain high-density samples, hot pressing was performed at 400°C for 30 min under a uniaxial pressure of 70 MPa, and subsequently, the furnace was cool down. The density of hot-pressed sample was estimated from its weight and size. The relative density of sample was 97.4%. The actual composition was analyzed by energy-dispersive X-ray spectroscopy (EDX) on a TM-3030 (Hitachi Hightech) equipped with an EDX-SwiftED analyzer (Oxford). The phase purity and the crystal structure of the Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 sample were examined by powder synchrotron XRD with an energy of 25 keV (λ = 0.495395 Å) at the beamline BL02B2 of SPring-8. The synchrotron XRD experiments were performed at room temperature with a sample rotator system, and the diffraction data were collected using a high-resolution one-dimensional semiconductor detector MYTHEN [Multiple mythen system] [30] with a step of 2θ = 0.006^o. The crystal structure parameters were determined by Rietveld analysis using the RIETAN-FP [31]. The crystal structure was depicted using VESTA [32].

To investigate the thermoelectric properties of sample, the electrical resistivity (ρ) and the Seebeck coefficient (S) were measured using the four-probe method under a helium atmosphere with a ZEM-3 (Advance Riko) instrument. The κ_total was calculated using the equation κ_total = DC_pd_s, where D, C_p and d_s are the thermal diffusivity, specific heat and sample density, respectively. D was measured by the laser-flash method with a TC1200-RH (Advance Riko) instrument. The C_p value of 0.20 Jg⁻¹K⁻¹ was obtained from the Dulong–Petit model, C_p = 3nR, where n is the number of atoms per formula unit and R is the gas constant. Noted that the actual C_p values of PbTe and PbSe increase few percent at high temperature [33,34], implying that the present C_p value could also be increased few percent at 723 K. Hall coefficient was measured using a physical property measurement system (PPMS, Quantum Design) at room temperature.

Results and discussion

Powder XRD patterns for Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 are shown in Figure 1. Although the peaks showed slightly asymmetry, the single-phase and no peak split were observed, indicating the homogeneity of the sample. Note that different compositional ratio of samples resulted in phase separation or inhomogeneity of the composition (Supplemental Fig. S1), thus we report the thermoelectric properties of above compositional sample which showed the best homogeneity. It has been reported that Pb(S/Te) with NaCl type has very low atomic solubility [35]. In this study as well, homogeneity sample was obtained with a composition in smaller ratio of Te than S, in which S and Te were 40% and 10%, respectively. XRD peaks of the phase can be indexed by the NaCl-type structural model (space group: Fm3m, #225). Lattice constant is estimated as 5.94858(5) Å. No compositional segregation was detected by EDX mapping (Fig. S2). The average chemical composition of the obtained sample is estimated as Ag_0.257(10)Pb_0.508(24)Bi_0.235(9)S_0.360(17)Se_0.520(7)Te_0.120(14). The obtained composition is almost same as the nominal composition, within the error of the equipment, thus to simplify, we call the sample Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 in this study. To estimate total ΔS_mix for our sample, ΔS_mix for both anionic and cationic sites were separately calculated using actual compositions. Subsequently, we took the sum of those values to obtain total ΔS_mix according to the following formula, which is based on our new concept of evaluating ΔS_mix (total) in compositionally and crystallographically complicated compounds [20]. $\mathrm{\Delta }{S}_{\text{mix}}\left(\text{total}\right)=\sum _{i=1}^n\mathrm{\Delta }{S}_{\text{mix}}^i$ where n is the number of crystallographically independent sites in the unit cell. Here, ΔSⁱ_mix is calculated by $\mathrm{\Delta }{S^i}_{\text{mix}}=-R\sum _{i=1}^N{x}_i\ln x_i$, where N and x_i are number of the component at the mixed site and the atomic fraction of the component, respectively. According to the above formula, present sample possesses ΔSⁱ_mix (cation Site) = 1.03R and ΔSⁱ_mix (anion site) = 0.96R, respectively (see inset of Figure 1). Finally, ΔS_mix (total) = 2.00R can be obtained. Let us mention that a similar situation has already been seen for CsCl-type superconductors (Sc,Zr,Nb,Ta)_0.65(Rh,Pd)_0.35 reported by Stolze et al [36] and NaCl-type MCh [22,28,29]. The obtained ΔS_mix exhibited the highest ΔS_mix (total) value among all HEA thermoelectric materials. A schematic image of crystal structure for MST-HEA MCh is shown in inset of Figure 1 together with its mother compound of PbSe.

Figure 1. Synchrotron X-ray diffraction patterns of Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10. Schematic images of crystal structure for PbSe and Multi-site-type high-entropy alloyed (MST-HEA) Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 with estimated ΔS_mix.

Figure 2(a) shows the temperature dependences of ρ and S above room temperature with the data of AgPbBiSe₃ (Ag_1/3Pb_1/3Bi_1/3Se) [11] as a reference. Compared to the upturn behavior of ρ for Ag_1/3Pb_1/3Bi_1/3Se, that for Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 linearly increased with increasing temperature, and the magnitude value was less than four times at around room temperature. The ρ values for present sample and Ag_1/3Pb_1/3Bi_1/3Se were 8.0 mΩcm and 17.3 mΩcm at around 723 K, respectively. To discuss the suppression of ρ with the actual carrier concentration, Hall effect measurement was performed at room temperature. The Hall coefficient (R_H) exhibited negative value, indicating the electron carrier is dominant. The estimated carrier concentration was 8.04 × 10¹⁹ cm⁻³, which is larger than that of 1.44 × 10¹⁸ cm⁻³ for Ag_1/3Pb_1/3Bi_1/3Se, indicating that the suppression of ρ is caused by increase of carrier concentration possibly due to the deficiency. Considering the increase of electron carrier, the deficiency of chalcogen elements and/or Ag¹⁺ is possible. On the other hand, carrier mobility of present sample (μ = 18.52 cm²V⁻¹s⁻¹) became lower than that of Ag_1/3Pb_1/3Bi_1/3Se (μ = 273.07 cm²V⁻¹s⁻¹). Lowering of mobility can be attributed to the increase of randomness by alloying and/or increase of carrier concentration. A negative value of the S also indicates the n-type polarity of the sample (Figure 2b). The magnitude of the S increased with increasing temperature. Unlike the ρ behavior, the S exhibited almost same trend as the reference and both values are close.

Figure 2. (a) Temperature dependence of the electrical resistivity and (b) Seebeck coefficient of Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 and Ag_1/3Pb_1/3Bi_1/3Se as a reference.

Figure 3(a) shows the temperature dependence of κ_total. Very low κ_total of less than 0.75 Wm⁻¹K⁻¹ is obtained at room temperature, which decreased with heating to 0.61 Wm⁻¹K⁻¹ at 723 K. The κ_L was determined by subtracting the electronic thermal conductivity (κ_e) from κ_total (Figure 4b). κ_e was estimated using the following Wiedemann–Franz law, κ_e = LTρ⁻¹, where L is the Lorenz number and estimated using an equation L = 1.5 + exp(–|S|/116) [37]. The value of κ_L at room temperature is around 0.62 Wm⁻¹K⁻¹ and decreased to 0.46 Wm⁻¹K⁻¹ at T = 723 K. Noted that the actual C_p values of PbTe and PbSe increase few percent at high temperature [33,34], implying that the present C_p value could also be increased few percent at 723 K. Contrast to the small temperature dependence of κ_L in Ag_1/3Pb_1/3Bi_1/3Se, the decrease of κ_L with increasing temperature indicates that the phonon scattering process is dominated by the Umklapp scattering process. Although the κ_L at room temperature showed some difference, they became almost same value at 723 K. In Ag_1/3Pb_1/3Bi_1/3Se [11], the fundamental origin of this ultra-low κ_L was explained by the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s² lone pairs of Bi and Pb. They revealed the existence of bonding heterogeneity, which is due to the presence of weak and strong bonding between the Se anion and cation with different electropositivity, using the first-principles density functional theory and electron localization function. In addition, the presence of 6s² lone pair electrons around Pb and Bi fosters the lattice anharmonicity, which also contributes the reduction of low lattice thermal conductivity. Considering the similarity between the Ag_1/3Pb_1/3Bi_1/3Se and present sample, we presumed the ultra-low κ_L for present sample is realized by the same situation. Compared to Ag_1/3Pb_1/3Bi_1/3Se, the present sample exhibited slightly higher lattice thermal conductivity, which is possibly due to the inclusion of lighter element of S with 40% in anion site. Note that, considering the inclusion of both lighter and heavier elements of S with 40% and Te with 10% in anion site, the suppression and enhancement of lowering for thermal conductivity also coexists. This might result in the similar values of κ_L between Ag_1/3Pb_1/3Bi_1/3Se and the present sample. In any case, various synergistic effects, different atomic weight, chemical disorder, solid-solution effect and bonding heterogeneity due to the introduction of MST-HEA would contribute to the suppression of κ_L. Further investigation for the quantification of the above components and the HEA effect in thermoelectric properties would be required for the development of HEA-type thermoelectric materials, for instance the systematic tuning of atomic weight with same ΔS value.

Figure 3. (a) Temperature dependences of thermal conductivity (κ_Total) and (b) lattice thermal conductivity (κ_L) for Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 and Ag_1/3Pb_1/3Bi_1/3Se as a reference.

Figure 4. (a) Temperature dependences of power factor (PF) and (b) figure of merit (ZT) for Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 and Ag_1/3Pb_1/3Bi_1/3Se as a reference.

Figure 4(a) shows the temperature dependences of the power factor (S²ρ⁻¹). The power factor increases with increasing temperature and reaches the maximum value of 4.4 μWcm⁻¹K⁻² at 723 K. The power factor of the sample exhibited over two times higher value within the measured temperature range. Contrast to the close value of S for both results, the around one-third of decrease of ρ for the obtained sample results in the enhancement of power factor. Figure 4(b) shows the temperature dependences of ZT. Relatively high ZT value of 0.54 was obtained at 723 K. The ZT value of the present sample exhibited higher than that of the reference at the measured temperature range.

Conclusion

We have synthesized polycrystalline sample of new multi-site-type high-entropy alloyed (MST-HEA) metal chalcogenide Ag_0.25Pb_0.50Bi_0.25S_0.40Se_0.50Te_0.10 with an NaCl-type structure using conventional solid-state reaction. For present sample, ΔS_mix reached 2.00R, which exceed ideal value of ΔS_mix = 1.79R for the single-site alloying with six different elements. The concept of MST-HEA in complicated compounds would be useful to develop new HEA-type thermoelectric materials with very high entropy of mixing. The Seebeck coefficient (S) and Hall coefficient demonstrated the nature of n-type polarity for the present sample. Compared to the upturn behavior of electrical resistivity (ρ) for Ag_1/3Pb_1/3Bi_1/3Se, the ρ linearly increased with increase in temperature for MST-HEA sample and the ρ was suppressed approximately one quarter than that of Ag_1/3Pb_1/3Bi_1/3Se without large decrease of S, resulted in the enhancement of power factor. The ultra-low κ_L around 0.62 Wm⁻¹K⁻¹ at room temperature and 0.46 Wm⁻¹K⁻¹ at T = 723 K were achieved possibly due to the synergistic presence of bonding heterogeneity and lattice anharmonicity arising from 6s² lone pairs of Bi and Pb. The ultra-low κ_L and relatively high ZT value suggest that this new MST-HEA MCh could be the promising candidate as an n-type thermoelectric material by further investigation of carrier tuning.

Acknowledgements

The authors thank T. Mitobe and K. Morino for supports in experiments.

Disclosure statement

Experimental data are available via reasonable requests to the corresponding author. No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JST-CREST (JPMJCR20Q4) and the Tokyo Metropolitan Government Advanced Research (H31-1).